We have calculated the emission line spectrum of neutral helium for densities up to Ne = 1014 cm−3 and for a large range in optical depth. All levels up to n = 100 are included, some specifically (up to n = 12) and others are combined into groups of fictitious levels. We made use of the newest collision strengths and took into account the transfer of all lines, using the local escape probability method. The model represents a major improvement over previous high density calculations that did not include some important processes, such as collisional ionization and three-body recombination. We used it to check the primordial helium abundance and found some low values, despite the improved 23S→33D collisional rate that we have used. The new results should help to explain the broad helium lines in the spectrum of AGNs, where extreme densities and optical depths are likely to occur. We also present a simplified scheme, which is accurate and easy to incorporate into existing photo-ionization codes. Full details of this scheme, including all atomic data, are given in an Appendix.